A(1). Field of the Invention
The invention relates to a decimation filter arrangement for reducing the sampling frequency of a time-discrete input signal from f.sub.i to f.sub.u. This input signal is formed by a sequence of input components which occur with the input sampling frequency f.sub.i. This input signal is converted into a time-discrete output signal consisting of a sequence of output components which occur with the output sampling frequency f.sub.u. A component of the input signal or output signal is to be understood to mean a quantity which characterizes the magnitude of an (analog) signal at a given instant. This quantity may assume any value in a predetermined interval or only a plurality of discrete values. In the latter case, the signal is commonly referred to as a digital signal and the component is usually represented by a code word comprising a number of bits.
A(2). Description of the Prior Art
Arrangements of the above-described type have been known for many years already. For further information, reference is made, for the sake of brevity, to references 1, 2, 3 and 4 of paragraph C. From these references it can be seen that such an arrangement produces an output signal whose output sampling frequency is a rational portion 1/M of the input sampling frequency; i.e. f.sub.u =f.sub.i /M, wherein M is an integer.
A practical implementation of a decimation filter arrangement is extensively described in, for example, reference 3. In order to get a clear picture of the operation of the known arrangement, the q.sup.th component of the input signal will hereinafter be designated x(q), wherein q=. . . -2, -1, 0, 1, 2, 3, . . . and the n.sup.th component of the output signal will be designated y(n), wherein n=. . . -2, -1, 0, 1, 2, 3, . . . . This prior art decimation filter arrangement comprises a signal store for storing N consecutive components of the input signal. In addition, it comprises a soefficient store in which a group of filter coefficients is stored, which group comprises N filter coefficients and wherein the m.sup.th filter coefficient will be designated a(m), wherein m=0, 1, 2, . . . N-1. This group of filter coefficients represents the finite impulse response of an FIR filter. In a multiplying arrangement the N input components stored in the signal store are each multiplied by an associated filter coefficient and the N products obtained are added together. The sum component obtained thereby represents an output components. More specifically, the relationship between the n.sup.th output component y(n) of the filter arrangement and the input components can mathematically be described as follows: ##EQU1##
From the above expression (1) it follows that the reduction factor M can only be an integer because otherwise nM-m is not an integer and because x(q) is only defined for integral values of q.
It should be noted that a change of the sampling frequency with a rational number L/M, wherein both L and M are integers, can be realised by arranging an interpolation filter arrangement which has an interpolation factor L in cascade with the decimation filter arrangement which has a decimation factor M. This is described extensively in the references 1 and 3. Reference 4 describes a decimation filter arrangement wherein in a particularly efficient manner a change of the sampling frequency with the rational factor L/M can be realised.
In practice it has been found that the are situations in which the sampling frequency of a signal must be changed by an irrational factor (for example 1/.sqroot.2. Such a situation occurs, for example, in digital audio equipment which must be intercoupled, for example, a digital tuner, a digital tape recorder, a digital pick-up apparatus, etc. In practice, these equipments each comprise there own clock pulse generators for generating the required sampling pulses. The frequencies of the clock pulse generators will never exactly be equal to each other and in practice cannot be made equal to each other. In order to render it possible for these equipments to co-operate with each other, the sampling frequency of the digital signal applied by a first equipment to a second equipment must be adapted to the sampling frequency of the second equipment.